The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275,what wavelength in mm of light has sufficient energy per photon to dislodge an electron from the surface of sodium
I got
430
n
m
Explanation:
You need
275
k
J
to dislodge one mol of electrons so we need:
275
×
10
3
6
×
10
23
=
4.6
×
10
−
19
J
for one electron only.
We can use Einstein`s relationship between energy
E
and frequency
f
and between frequency and wavelength
λ
:
E
=
h
f
=
h
c
λ
to find the wavelength (
h
is Plank`s Constant and
c
the speed of light).
We get:
λ
=
h
c
E
=
(
6.6
×
10
−
34
)
⋅
3
×
10
8
4.6
×
10
−
19
=
4.3
×
10
−
7
m
=
430
n
m
To determine the wavelength of light required to dislodge an electron from the surface of sodium, we can use the following equation:
E = hc/λ
Where:
E is the energy required to dislodge electrons (275 eV)
h is Planck's constant (6.626 x 10^-34 J·s)
c is the speed of light (2.998 x 10^8 m/s)
λ is the wavelength of the light in meters
First, let's convert the energy required from electron volts (eV) to joules (J):
1 eV = 1.60219 x 10^-19 J
Therefore, the energy required in joules (E) is:
E = 275 eV × 1.60219 x 10^-19 J/eV = 4.40548 x 10^-17 J
Now we can rearrange the equation to solve for the wavelength (λ):
λ = hc/E
Plugging in the values:
λ = (6.626 x 10^-34 J·s) × (2.998 x 10^8 m/s) / (4.40548 x 10^-17 J)
Calculating this expression, we find:
λ = 4.527 x 10^-7 meters
To convert this value to millimeters (mm), we can multiply by 1000:
λ = 4.527 x 10^-7 meters × 1000 = 0.4527 mm
Therefore, the wavelength of light required to dislodge an electron from the surface of sodium is approximately 0.4527 mm.
To determine the wavelength of light required to dislodge an electron from the surface of sodium, we can use the equation:
E = hc/λ
Where:
E is the energy required to dislodge an electron (275 eV in this case)
h is Planck's constant (6.626 x 10^-34 Js)
c is the speed of light (3.00 x 10^8 m/s)
λ is the wavelength of light we want to find
First, we need to convert the energy from electron volts (eV) to joules (J). Since 1 eV is equal to 1.602 x 10^-19 J, we have:
E = 275 eV * 1.602 x 10^-19 J/eV
E ≈ 4.41 x 10^-17 J
Now we can rearrange the equation to solve for the wavelength:
λ = hc/E
λ = (6.626 x 10^-34 Js * 3.00 x 10^8 m/s) / (4.41 x 10^-17 J)
λ ≈ 4.51 x 10^-7 m
To convert the wavelength to millimeters (mm), we divide by 10^-3:
λ ≈ (4.51 x 10^-7 m) / (10^-3)
λ ≈ 4.51 x 10^-4 mm
Therefore, the wavelength of light that has sufficient energy per photon to dislodge an electron from the surface of sodium is approximately 4.51 x 10^-4 mm.